New Geometry (新几何) invented by Zhang JingZhong (張景中) derived from 2 basic theorems:
1) Triangles internal angles =180º
2) Triangle Area = ½ base * height
=> derive all geometry
=> trigonometry
=> algebra
(These 3 maths are linked, unlike current syllabus taught separately)
The powerful Area (Δ) Proof Techniques:
1) Common Height:
Line AMB, P outside line
Δ PAM / Δ PBM = AM/BM
2) Common 1 Side (PQ):
Lines AB and PQ meet at M
Δ APQ /Δ BPQ = AM/BM
3) Common 1 Angle:
∠ABC=∠XYZ (or ∠ABC+∠XYZ = ∏ )
Δ ABC /Δ XYZ= AB.BC /XY.YZ
These 3 theorems can prove Butterfly and tough IMO problems.
